Elsayed, A.; Grimble, M. J. A new approach to the \(H_{\infty}\) design of optimal digital linear filters. (English) Zbl 0678.93063 IMA J. Math. Control Inf. 6, No. 2, 233-251 (1989). Summary: A novel approach to the solution of the \(H_{\infty}\) estimation problem is developed. The solution is arrived at by embedding the problem within a fictitious mathematically equivalent \(\ell_ 2\) framework in which a stable prefilter is introduced at the input of each noise source. The development is straightforward and relies on a polynomial system technique. Two numerical examples are presented to demonstrate the proposed approach. Cited in 66 Documents MSC: 93E11 Filtering in stochastic control theory 93E10 Estimation and detection in stochastic control theory 46J15 Banach algebras of differentiable or analytic functions, \(H^p\)-spaces PDF BibTeX XML Cite \textit{A. Elsayed} and \textit{M. J. Grimble}, IMA J. Math. Control Inf. 6, No. 2, 233--251 (1989; Zbl 0678.93063) Full Text: DOI OpenURL